In this paper we present concentration inequalities for the hidden layers and the output of a generic SDNN based on the ideas of norm-subGaussian distribution and of weak martingale. We introduce the notion of expected classifier and give a probabilistic bound to its classification error. We also find – via an optimal stopping procedure – the number of layers for the SDNN that strikes the perfect balance between computational cost and accuracy of the analysis. Finally, we apply our findings to a stochastic version of the FNNRA of [1]}. In future work, we plan to explore the geometric properties of SDNNs, in the spirit of [2]}, [3]}, [4]}.
